I love Thunderbird. I love using Google Desktop with it - two whaps at the "Ctrl" button and I get my search box, and I'm seconds away from finding any message.
Unfortunately, Google Desktop still doesn't index documents attached to email messages stored in Thunderbird. It's fine with attachments to email messages stored in Outlook, but Thunderbird remains unsupported. And I absolutely refuse to use Outlook.
After several ridiculous efforts including downloading messages into Eudora (which stores files in an "attachments" directory that's easily indexed by Google) but reading them in Thunderbird, trying Penelope (Eudora overlay for Thunderbird which doesn't seem to do anything of value), I found another ridiculous workaround that actually works almost easily: Attachment Extractor.
Attachment Extractor has a huge number of options, including "Auto-Extract", which will automatically store attachments in a directory you identify. It's pretty smart - appends a number to files so nothing gets overwritten, that kind of thing. It gets my stamp of approval.
Comments